Auto mode should result in more flashes, because the thyristor circuitry
should quench the flash and recycle the unused current back into the
capacitor.  The power savings varies based on how quickly the flash is
quenched (flash with subjects that are close usually requires less light).

By comparison, the flash uses all of the capacitor's stored power when it is
is manual mode.  The photographer limits the amount of light entering the
camera, not by having the flash cut off early, but by stopping down the lens
aperture.

So, unless I've missed something, you should see more flashes in automatic
mode, since not every flash consumes as much power as manual flashing.